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MANAGERIAL ECONOMICS
SHORT ANSWER (5 pts each)
1. Production Function Concepts. Indicate whether each of the following statements is true or false.
A. Decreasing returns to scale and declining average costs are indicated when εQ < 1.
B. If the marginal product of capital falls as capital usage grows, the returns to capital are decreasing.
C. L-shaped isoquants describe production systems in which inputs are perfect substitutes.
D. Marginal revenue product measures the profit earned through expanding input usage.
E. The marginal rate of technical substitution will be affected by a given percentage increase in the marginal productivity of all inputs.
1. SOLUTION
A. True. When εQ < 1, the percentage change in output is less than a given percentage change in all inputs. Thus, decreasing returns to scale and increasing average costs are indicated.
B. True. Returns to the capital input factor are decreasing when the marginal product of capital falls as capital usage grows.
C. False. L-shaped production isoquants reflect a perfect complementary relation among inputs.
D. False. Marginal revenue product is the revenue generated by expanding input usage, and represents the maximum that could be paid to expand usage. Since MRP is calculated before input costs (wages in the case of labor, for example), it does not measure the increase in profit earned through expansion.
E. False. The marginal rate of technical substitution is measured by the relative marginal productivity of input factors. This relation is unaffected by a commensurate increase in the marginal productivity of all inputs.
2. Cost Curves. Indicate whether each of the following involves an upward or downward shift in the long-run average cost curve or, instead, involves a leftward or rightward movement along a given curve. Also indicate whether each will have an increasing, decreasing, or uncertain effect on the level of average cost.
A. A rise in wage rates
B. A decline in output
C. An energy-saving technical change
D. A fall in interest rates
E. An increase in learning or experience
2. SOLUTION
A. A rise in wage rates will cause an upward shift in the LRAC curve, and increase LRAC.
B. A decline in output will be reflected in a leftward movement along a given LRAC curve, and involve an uncertain effect on the level of LRAC.
C. Energy-saving technical change will cause a downward shift in the LRAC curve, and decrease LRAC.
D. A fall in interest rates gives rise to a downward shift in the LRAC curve, and a decrease in LRAC.
E. Learning, like any beneficial technical change or innovation, will cause a downward shift in the LRAC curve, and decrease LRAC.
3. Market Structure Concepts. Indicate whether each of the following statements is true or false.
A. In long-run equilibrium, every firm in a perfectly competitive industry earns zero profit. Thus, if price falls, none of these firms will be able to survive.
B. Pure competition exists in a market when all firms are price takers as opposed to price makers.
C. A natural monopoly results when the profit-maximizing output level occurs at a point where long-run average costs are declining.
D. Downward-sloping industry demand curves characterize both perfectly competitive and monopoly markets.
E. A decrease in the price elasticity of demand would follow an increase in monopoly power.
3. SOLUTION
4. SOLUTION
A. Increase. As import quotas are decreased, fewer substitutes for domestic automobiles become available. This will decrease competition in the industry, and ease pressure on profit margins.
B. Increase. An elimination of uniform emission standards reduces product homogeneity. As product differentiation rises, some increase in the pricing discretion of firms will result.
C. Decrease. An increase in automobile price advertising increases price competition in the industry and thereby decrease the ability of firms to raise prices and profit margins.
D. Increase. An increase in import tariffs (taxes) increases the price of import cars, thus making imports less attractive to car buyers. This will reduce the price pressure on domestic manufacturers, and make it easier for them to increase profit margins.
E. Decrease. A rising value of the dollar that has the effect of lowering import car prices puts downward pressure on the profit margins of domestic manufacturers.
5. Costs of Regulation. People of many different age groups and circumstances take advantage of part-time employment opportunities provided by the fast-food industry. Given the wide variety of different fast-food vendors, the industry is fiercely competitive, as is the so-called unskilled labor market. In each of the following circumstances, indicate whether the proposed changes in government policy is likely to have an increasing, decreasing, or uncertain effect on employment opportunities in this industry.
A. Elimination of minimum wage law coverage for those working less than 20 hours per week.
B. An increase in spending for education that raises basic worker skills.
C. An increase in the employer portion of federally mandated FICA insurance costs.
D. A requirement that employers install expensive new worker-safety equipment.
E. A state requirement that employers pay 8 percent of wages to fund a new national health care program.
5. SOLUTION
A. Uncertain. Elimination of minimum wage coverage for those working less than 20 hours per week will either increase or have no effect on employment opportunities in the industry. If the minimum wage is at the current market wage rate, an increase will have the effect of reducing employment opportunities. However, if the minimum wage rate is below the current market wage rate, as has been true in many parts of the U.S. during the 1980s and 1990s, an increase will have no effect.
B. Increase. An increase in spending for education that raises basic worker skills has the effect of increasing the marginal productivity of workers, and the marginal revenue product generated for employers. A favorable impact on job opportunities can be expected as a result of such an enhancement in worker efficiency.
C. Decrease. An increase in the employer portion of federally-mandated FICA insurance costs has the effect of increasing the costs of worker employment. Without any similar enhancement in worker productivity, a negative impact on employment opportunities can be anticipated.
D. Uncertain. A requirement that employers install expensive new worker- safety equipment has an uncertain effect on employment opportunities. Generally speaking, a reduction in employment opportunities can be expected following an increase in such costs. However, if the mandated increase results in a rise in fixed costs only, and if the industry earned above-normal rates of return on investment, then employers might pay such costs with no reduction in employment.
E. Decrease. Like an increase in the employer portion of federally-mandated FICA insurance costs, a state requirement that employers pay 8 percent of wages to fund a new national health care program has the effect of increasing the costs of worker employment. Without any offsetting enhancement in worker productivity, a negative impact on employment opportunities can be anticipated.
D. False. A project which has NPV > 0 using the risk adjusted discount rate approach has an α factor below the maximum acceptable level. Such a project will be desirable, since it has a "price per risky dollar of return" below that necessary to induce investment.
E. True. State lotteries that pay back 50 percent of the amount bet involve players who have an α > 2.
SHORT PROBLEMS (10 pts each)
7. Optimal Price. Payless Shoe Stores, Inc., cut prices on women's dress shoes by 2 percent during the first quarter and enjoyed a 4 percent increase in unit sales over the period as compared to a year earlier.
A. Calculate the point price elasticity of demand for Payless shoes.
B. Calculate the company's optimal shoe price if marginal cost is $10 per unit.
7. SOLUTION
A. εP =
Percentage change in output Percentage change in price
B. The profit maximizing price can be found as follows:
MC = MR
$10 = P(1 % 1
εP
$10 = P(1 %
$10 = 0.5P
P = $
8. Optimal Input Level. Ticket Services, Inc., offers ticket promotion and handling services for concerts and sporting events. The Chicago branch office makes
heavy use of spot radio advertising on WNDY-AM, with each 30-second ad costing $100. During the past year, the following relation between advertising and ticket sales per event has been observed:
Sales (units) = 5,000 + 100A - 0.5A^2.
Here A represents a 30-second radio spot ad, and sales are measured in numbers of tickets.
Harry Stone, manager for the Chicago office, has been asked to recommend an appropriate level of advertising. In thinking about this problem, Stone noted its resemblance to the optimal resource employment problem he had studied in a managerial economics course that was part of his MBA program. The advertising/sales relation could be thought of as a production function, with advertising as an input and sales as the output. The problem is to determine the profit-maximizing level of employment for the input, advertising, in this "production" system. Stone recognized that to solve the problem, he needed a measure of output value. After reflection, he determined that the value of output is $2 per ticket, the net marginal revenue earned by Ticket Services (price minus all marginal costs except advertising).
A. Continuing with Stone's production analogy, what is the "marginal product" of advertising?
B. What is the rule for determining the optimal amount of a resource to employ in a production system? Explain the logic underlying this rule.
C. Using the rule for optimal resource employment, determine the profit- maximizing number of radio ads.
8. SOLUTION
A. The marginal product of advertising is given by the expression:
MP A = ∆S/∆A
= 100 - A
B. The rule for determining the optimal amount of a resource to employ is:
MRP A = P A
The logic of this rule can be best understood by simply dissecting the above relations:
MRP A = P A
A. The perfectly competitive firm will supply output so long as it is profitable to do so. Since P = MR in perfectly competitive markets, the firm supply curve is given by the relation:
P = MC = ∆TC/∆Q = $1 + $0.000016Q
when quantity is expressed as a function of price, the firm supply curve is:
P = $1 + $0.000016Q
0.000016Q = -1 + P
QS = -62,500 + 62,500P
B. If the company is one of 500 such competitors, the industry supply curve is found by simply multiplying the firm supply curve derived in Part A by
- This is equivalent to a horizontal summation of all 500 individual firm supply curves. When quantity is expressed as a function of price:
QS = 500(-62,500 + 62,500P)
= -31,250,000 + 31,250,000P
When price is expressed as a function of quantity:
QS = -31,250,000 + 31,250,000P
31,250,000P = 31,250,000 + QS
P = $0.000000032QS
C. QS = -31,250,000 + 31,250,000P
10. Certainty Equivalent Method. Tex-Mex, Inc., is a rapidly growing chain of Mexican-food restaurants. The company has a limited amount of capital for expansion and must carefully weigh available alternatives. Currently, the company is considering opening restaurants in Santa Fe or Albuquerque, New Mexico. Projections for the two potential outlets are as follows:
Annual Profit City Outcome Contribution Probability
Albuquerque Failure $100,000 0. Success 200,000 0. Santa Fe Failure $ 60,000 0. Success 340,000 0.
Each restaurant would require a capital expenditure of $700,000, plus land acquisition costs of $500,000 for Albuquerque and $1 million for Santa Fe. The company uses the 10-percent yield on riskless U.S. Treasury bills to calculate the risk-free annual opportunity cost of investment capital.
A. Calculate the expected value, standard deviation, and coefficient of variation for each outlet's profit contribution.
B. Calculate the minimum certainty equivalent adjustment factor for each restaurant's cash flows that would justify investment in each outlet.
C. Assuming that the management of Tex-Mex is risk averse and uses the certainty equivalent method in decision making, which is the more attractive outlet? Why?
10. SOLUTION
A. Albuquerque
E(πA) = $100,000(0.5) + $200,000(0.05) = $150,
σA = ($100,000 & $150,000)^2 (0.05)
______________________________
+ ($200,000 - $150,000)^2 (0.05)
VA = σA/E(πA) = 0.
Santa Fe
E(πSF ) = $60,000(0.5) + $340,000(0.5) = $200,
σSF = ($60,000 & $200,000)^2 (0.05)
_____________________________
+ ($340,000 - $200,000)^2 (0.5)
MR = $1,000 - $0.03Q.
Relevant total cost, marginal cost, and profit functions are:
TC = $1,500,000 + $600Q + $0.005Q^2 ,
MC = $600 + $0.01Q,
π = TR - TC,
= -$0.02Q^2 + $400Q - $1,500,000.
A. Calculate the profit-maximizing activity level for Simpson Flanders when the firm is operated as an integrated unit.
B. Assume that the company is reorganized into two independent profit centers with the following cost conditions:
TCMfg. = $1,250,000 + $500Q + $0.005Q^2 ,
MC (^) Mfg. = $500 + $0.01Q,
and,
TCDist. = $250,000 + $100Q,
MC (^) Dist. = $100.
Calculate the transfer price that ensures a profit-maximizing level of profit for the firm, with divisional operation based on the assumption that all output produced is to be transferred internally.
C. Now assume that a major distributor in the European market offers to buy as many valves as Simpson Flanders wishes to offer at a price of $645. No impact on demand from the company's North American customers is expected, and current facilities can be used to supply both markets. Calculate the company's optimal price(s), output(s), and profits in this situation.
11. SOLUTION
A. Profit maximization occurs at the point where MR = MC, so the optimal output level is:
MR = MC,
$1,000 - $0.03Q = $600 + $0.01Q,
400 = 0.04Q,
Q = 10,000.
This implies:
P = $1,000 - $0.015(10,000),
π = TR - TC,
= -$0.02(10,000^2 ) + $400(10,000) - $1,500,000.
B. To derive an appropriate transfer price when no external market is present, the net marginal revenue for the distribution division is set equal to marginal cost of the manufacturing division to identify the firm's profit- maximizing activity level:
MR - MC (^) Dist. = MCMfg.,
$1,000 - $0.03Q - $100 = $500 + $0.01Q,
400 = 0.04Q,
Q = 10,000.
The 10,000-unit output level remains optimal for profit maximization, as must be the case. If the distribution division determines the quantity it will purchase by movement along its marginal revenue curve, and the manufacturing division supplies output along its marginal cost curve, then the market clearing transfer price is the price that results when MR - MC (^) Dist. = MCMfg. At 10,000 units of output, the optimal transfer price is:
P (^) T = MCMfg.,
At a transfer price of $600, the quantity supplied by the manufacturing division equals 10,000. Similarly, the quantity demanded by the distribution division also equals 10,000 at a transfer price of $600:
MR - MC (^) Dist. = P (^) T ,
Maximum total profits are:
π = TRNA + TRE - TCMfg. - TCDist.,
- $500(14,500) - $0.005(14,5002)^ - $250,
The offer from the European distributor should be accepted as it results in a $135,000 increase in profits, from $500,000 to $635,000. Notice that the optimal transfer price P (^) T = $645 equates the marginal cost of the each division to the marginal revenue derived from each market. Given the separate nature of the North American and European markets, the company is able to grow and profitably segment its market at the same time.
